Vocabulary for solving word problems

My students had been struggling with how to solve addition and subtraction word problems for what seemed like forever. They could underline the question and they could find the numbers. Most of the time, my students just added the two numbers together without making sense of the problem.

Ugh.

Can you relate?

Below are five math problem-solving strategies to use when teaching word problems on addition and subtraction using any resource.

So, how do I teach word problems? It’s quite complex, but so much fun, once you get into it.

How to teach addition and subtraction word problems

The main components of teaching addition and subtraction word problems include:

1. Teaching the Relationship of the Numbers – As a teacher, know the problem type and help students solve for the action in the problem
2. Differentiate the Numbers – Give students just the right numbers so that they can read the problem without getting bogged down with the computation
3. Use Academic Vocabulary – And be consistent in what you use.
4. Stop Searching for the “Answer” – it’s not about the answer; it’s about the process
5. Differentiate between the Models and the Strategies – one has to do with the relationship between the numbers and the other has to do with how students “solve” or compute the problem.

I am a big proponent of NOT teaching keyword lists. It just doesn’t work consistently across all problems. It’s a shortcut that leads to breakdowns in mathematical thinking. Nor should you just give students word problem worksheets and have them look for word problem keywords. I talk more in-depth about why it doesn’t work in The Problem with Using Keywords to Solve Word Problems.

Teach the Relationship of the Numbers in Math Word Problems

One way to help your students solve word problems is to teach them the relationship of the numbers. In other words, help them understand that the numbers in the problem are related to each other in some way.

I teach word problems by removing the numbers. Sounds strange right?

Removing the distraction of the numbers helps students focus on the situation of the problem and understand the action or relationship of the numbers. It also keeps students from solving the problem before we talk about the relationship of the numbers.

When I teach word problems, I give students problems with blank spaces and no numbers. We first talk about the action in the problem. We identify whether something is being added to or taken from something else. That becomes our equation. We identify what we have to solve and set up the equation with blank spaces and a square for the unknown number

___ + ___ = unknown

Do you want a free sample of the word problems I use in my classroom?  Click the link or the image below. FREE Sample of Word Problems by Problem Type

Differentiate the numbers in the Word Problems

Only after we have discussed the problem do I give students numbers. I differentiate numbers based on student needs. At the beginning of the year, we all do the same numbers, so that I can make sure students understand the process.

After students are familiar with the process, I start to give different students different numbers, based on their level of mathematical thinking.

I also change numbers throughout the year, from one-digit to two-digit numbers. The beauty of the blank spaces is that I can put any numbers I want into the problem, to practice the strategies we have been working on in class.

At some point, we do create a list of words, but not a keyword list. We create a list of actions or verbs and determine whether those actions are joining or separating something. How many can you think of?

Here are a few ideas:

Join: put, got, picked up, bought, made
Separate: ate, lost, put down, dropped, used

Don’t be afraid to use academic vocabulary when teaching word problems

I teach my students to identify the start of the problem, the change in the problem, and the result of the problem. I teach them to look for the unknown.

These are all words we use when solving problems and we learn the structure of a word problem through the vocabulary and relationship of the numbers.

In fact, using the same vocabulary across problem types helps students see the relationship of the numbers at a deeper level.

Take these examples, can you identify the start, change and result in each problem? Hint: Look at the code used for the problem type in the lower right corner.

For compare problems, we use the terms, larger, smaller, more and less. Try out these problems and see if you can identify the components of the word problems.

Stop searching for “the answer” when solving word problems

This is the most difficult misconception to break.

Students are not solving a word problem to find “the answer”. Although the answer helps me, the teacher, understand whether or not the student understood the relationship of the numbers, I want students to be able to explain their process and understand the depth of word problems.

Okay, they’re first and second-graders. I know.

My students can still explain, after instruction, that they started with one number. The problem resulted in other another number. Students then know that they are searching for the change between those two numbers.

It’s all about the relationship.

Differentiate between the models and the strategies

A couple of years ago, I came across this article about the need to help students develop adequate models to understand the relationship of the numbers within the problem.

A light bulb went off in my head. I needed to make a distinction between the models students use to understand the relationship of the numbers in the problem and the strategies to solve the computation in the problem. Models and strategies work in tandem but are very different.

Models are the visual ways problems are represented. Strategies are the ways a student solves a problem, putting together and taking apart the numbers.

The most important thing about models is to move away from them. I know that sounds odd.

You spend so long teaching students how to use models and then you don’t want them to use a model. Well, actually, you want students to move toward efficiency.

Younger students will act out problems, draw out problems with representations, and draw out problems with circles or lines. Move students toward efficiency. As the numbers get larger, the model needs to represent the relationship of the numbers

This is a prime example of moving from an inverted-v model to a bar model.

Here is a student moving from drawing circles to using an inverted-v.

Students should be solidly using one model before transitioning to another.  They may even use two at the same time while they work out the similarities between the models.

Students should also be able to create their own models. You’ll see how I sometimes gave students copies of the model that they could glue into their notebooks and sometimes students drew their own model.  They need to be responsible for choosing what works best for them. Start your instruction with specific models and then allow students to choose one to use. Always move students toward more efficient models.

The same goes for strategies for computation. Teach the strategies first through the use of math fact practice, before applying it to word problems so that students understand the strategies and can quickly choose one to use. When teaching, focus on one or two strategies. Once students have some fluency in a few strategies, have them choose strategies that work for different problems.

Which numbers do you put in the blank spaces?

Be purposeful in the numbers that you choose for your word problems. Different number sets will lend themselves to different strategies and different models. Use number sets that students have already practiced computationally.

If you’ve been taught to make 10, use numbers that make 10. If you’re working on addition without regrouping, use those number sets. The more connections you can make between the computation and the problem-solving the better.

The examples above are mainly for join and separate problems. It’s no wonder our students have so much difficulty with compare problems since we don’t teach them to the same degree as join and separate problems.

Our students need even more practice with those types of problems because the relationship of the numbers is more abstract. I’m going to leave that for another blog post, though.

Do you want a FREE sample of the resource that I use to teach Addition & Subtraction Word Problems by Problem Type?  Click this link or the image below.

How to Purchase the Addition & Subtraction Word Problems

The full resource is also available in my store for purchase and on Teachers Pay Teachers.

More Ideas for Teaching Word Problems

Word problems are widely seen in our classrooms today. Many children seem to struggle with how to go about solving these problems. However, it is so important for students to understand how to have access to these problems because they greatly improve strategic thinking and problem solving skills.

Below are summaries of two articles that I have reviewed. They discuss the importance of word problems and how to go about helping students best solve them. Through these articles, tips, and examples, you as parents should begin to understand why word problems are so important to your children in today’s classroom.

Article One: “Word Problem-Solving Instruction in Inclusive Third-Grade Mathematics Classrooms”

Summary: This article discusses the two methods of solving word problems in hopes to prove, through a study, that one way is more beneficial than the other. These two methods include; General Strategy Instruction (GSI) and Schema Based Instruction (SBI). GSI includes students using a four step process to solve word problems; understanding the problem, devising a plan, carrying out the plan, and looking back and reflecting. According to the article this is the process most commonly seen in our school textbooks. Likewise, the four steps in an SBI approach to word problems include; problem schema identification, representation, planning, and solution. One of the biggest ideas of this method is that there must be visual representation of a problem.

The article then goes into a study done in a third grade classroom, comparing the two methods of solving word problems over a long period time. The results of the study found that one way was not significantly better than the other at helping children increase their problem solving skills. As of now, this shows that both ways are successful at teaching students word problems. The article did prove that their are a variety of successful ways and as a teacher it is my hope to pick the one that will best benefit my students.

Article Two: Comprehension of Arithmetic Word Problems: A Comparison of Successful and Unsuccessful Problem Solvers

Summary: This article also discusses two ways to solve word problems. One of the ways is “Direct-Translation Strategy” (DTS), which the article calls an unsuccessful way, and the other is called “Problem Model Strategy,” (PMS), which the author calls the successful way. In the DTS strategy the student bases his/her solution on the selection of numbers and keywords from the problem. In the PMS strategy the learner creates a mental model of the situation being described in the problem.

Strategies/Tips for solving word problems:

1. Read the problem extra carefully. Sometimes you may need to read it a few times to understand it.
2. List all the information you can identify, including the units being used.
3. Look for keywords that will help you identify which operation you will be using (subtraction = how many will be left, difference).
4. Use sketches, drawings, and models.
5. To check to see if your answer is right, try doing the problem backwards starting with your answer.
6. Descriptive words can sometimes represent a relationship.
7. Identify the information that is still needed.

Vocabulary signposts in word problems:

Practice Word Problems:

Number Theory

• Heather has one whole pepperoni pizza. She wants to given an equal fraction of the pizza to herself and her two other friends. What fraction of the pizza will each person receive? (write your answer in fraction form)

Measurement

• Tom started playing his soccer game at 5 after 2  on Sunday afternoon, and his soccer game lasted 1 hour and 30 minutes. What time was Tom’s soccer game over?

Geometry

• Mrs. Smith wants to buy soil for her flower and vegetable fields. The length of the field is 25 feet and the width is 40. How much soil will she need to buy? If the soil costs $7.00 per 30 cubic feet, how much money will she be spending? Write your answers in a decimal to the nearest tens place.

Data Analysis and Probability

• Mark is the star player on his basketball team. In the last five games he has scored 17, 23, 16, 31, and 27 points. What is the average number of points he scored in the five games. What is the median number of points?

Algebraic Thinking

• There are 75 fifth graders at Northern Elementary School. They need to be split equally between lunch periods. This makes 25 students to be at each lunch period. Write an equation showing how many lunch periods there would need to be in order to have 25 students in each. Now solve the equation. How many lunch periods do you actually need?

References

1. Foye, B. (n.d.). Key Words in Math Word Problems. WISC-Online. Retrieved April 12, 2015, from http://www.wisc-online.com/Objects/ViewObject.aspx?ID=ABM1401
2. Griffin, C., & Jitendra, A. (2009). Word Problem-Solving Instruction in Inclusive Third-Grade Mathematics Classrooms. Journal of Educational Research, 102(3), 187-201. Retrieved April 15, 2012, from the EBSCOhost database.
3. Hegarty, M., Mayer, R., & Monk, C. (1995). Comprehension of Arithmetic Word Problems: A Comparison of Successful and Unsuccessful Problem Solvers. Journal of Educational Psychology, 87(1), 18-32.
4. 12 Tips For Solving Word Problems: Teaching Children How to Solve Mathematics Problems | Suite101.com. (n.d.). David R. Wetzel Writing Profile | Suite101.com. Retrieved April 15, 2012, from http://david-r-wetzel.suite101.com/12-tips-for-solving-word-problems-a57713